# conchoid

Definition from Wiktionary, the free dictionary

## Contents

## English[edit]

### Etymology[edit]

From Latin *concha* (“mussel”) (from Ancient Greek *κόνχη* (kónkhē)) + *-oid*, referring to the curved outline of a mussel shell.

### Noun[edit]

**conchoid** (*plural* **conchoids**)

- (mathematics, geometry) Any of a family of curves defined as the locus of points
*p*, such that each*p*is on a line that passes through a given fixed point*P*and intersects a given curve,*C*, and the distance from*p*to the point of intersection with*C*is a specified constant (note that for nontrivial cases two such points*p*satisfy the criteria, and the resultant curve has two parts).*The***conchoid**of a circle with respect to a point on the circle is a cardioid if the fixed distance is equal to the diameter of the circle.*The Conchoid of Nicomedes is the***conchoid**of a straight line with respect to a point not on the line.

**1815**, Charles Hutton,*Pappus*, entry in*A Philosophical and Mathematical Dictionary*, Volume 2, page 147,- He next treats of the properties of the
**Conchoid**, which Nicomedes invented for doubling the cube; applying it to the solution of certain problems concerning Inclinations, with the finding of two mean proportionals, and cubes in any proportion whatever.

- He next treats of the properties of the
**1982**, J. Lee Kavanau,*Curves and Symmetry*, Volume 1, page 3,- The classical
**conchoid**construction is a*non-orthogonal**polar-curvilinear*construction in which equal distances along a line are marked off from its point of intersection with a curve for various positions of the line as it rotates about a point.

- The classical
**2007**, James Stewart,*Single Variable Calculus*, Volume 2, page 662,- These curves are called
**conchoids of Nicomedes**after the ancient Greek scholar Nicomedes. He called them**conchoids**because the shape of their outer branches resembles that of a conch shell or mussel shell.

- These curves are called
**2009**, Niccolò Guicciardini,*Isaac Newton on Mathematical Certainty and Method*, page 68,- One of the best choices is the
**conchoid**, according to Newton the simplest curve after the circle.

- One of the best choices is the

- (geology) A conchoidal fracture in rock.
**1948**, Tennessee Valley Authority,*The Hiwassee Valley Projects*, Technical Report, Issue 5, Volume 2, page 359,**Conchoids**of sound rock, from a few feet to 20 or more feet in diameter, entirely surrounded by comparatively thin layers of weathered material, were frequently encountered, sometimes in adjacent series.

#### Usage notes[edit]

The fixed point (*P*) of the construction may be referred to as the *focus* of the **conchoid**; it may also be defined as the origin (of a Cartesian coordinate system) or the pole (if polar coordinates are used), and potentially referred to accordingly. The curve *C* is an example of a directrix.

#### Derived terms[edit]

- conchoid of de Sluze (strictly a cissoid)
- conchoid of Dürer (not actually a conchoid)
- conchoid of Nicomedes